Yes, some ISP's do block port 5001. Fortunately, you can change this port to work around the problem
Unless you have some weird and unusal firewall settings on your SMC router, then this will not be the cause of your problem. It might be worth checking you have UPnP enabled though.
I strongly suggest you login to the SlingBox support page both BEFORE and AFTER you make the changes to your SlingBox port - to be doubly sure there are no other problems: http://support.slingbox.com. Once you have logged in and registered your slingbox, you will see various info about your box including, very importantly, the Internet Viewing status. Check everything is good before, then after you've made the changes.
The following article describes changing your SlingBox port (don't forget, importantly, to fully re-run the Internet Viewing wizard!)... https://community.sling.com/thread/1456